Difference between revisions of "APN functions obtained via polynomial expansion in small dimensions"

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(Created page with "<table> <tr> <th>ID</th> <th>Representative</th> <th>Equivalent to</th> <th>Orthoderivative diff. spec.</th> </tr> <tr> <td>8.1</td> <td><math>\alpha^{170}x^{192} + \alpha^{85...")
 
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<td>SW 20</td>
 
<td>SW 20</td>
 
<td><math>0^{39692}, 2^{19752}, 4^{4756}, 6^{978}, 8^{72}, 10^{26}, 12^4</math></td>
 
<td><math>0^{39692}, 2^{19752}, 4^{4756}, 6^{978}, 8^{72}, 10^{26}, 12^4</math></td>
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</tr>
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</table>
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<table>
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<th>ID</th>
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<th>Representative</th>
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<th>Equivalent to</th>
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<th>Orthoderivative diff. spec.</th>
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</tr>
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<tr>
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<td>9.1</td>
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<td><math>\alpha^{365}x^{257} + x^{96} + x^{68} + \alpha^{219}x^{33} + x^5</math></td>
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<td>I 4</td>
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<td><math>0^{158529}, 2^{80829}, 4^{18144}, 6^{3283}, 8^{469}, 10^{294}, 12^{84}</math></td>
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</tr>
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<tr>
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<td>9.2</td>
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<td><math>\alpha^{438}x^{129} + x^{66} + \alpha^{219}x^{10} + x^3</math></td>
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<td>I 8</td>
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<td><math>0^{159418}, 2^{79275}, 4^{18690}, 6^{3213}, 8^{742}, 10^{252}, 12^{21}, 16^{21}</math></td>
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</tr>
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<tr>
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<td>9.3</td>
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<td><math>x^{136} + x^{24} + x^{17} + \alpha^{73}x^{10} + x^3</math></td>
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<td>I 3</td>
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<td><math>0^{159684}, 2^{78687}, 4^{19089}, 6^{3136}, 8^{777}, 10^{147}, 12^{84}, 14^{28}</math></td>
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</tr>
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<tr>
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<td>9.4</td>
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<td><math>x^{68} + \alpha^{73}x^{40} + x^{33} + x^5</math></td>
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<td>I 10</td>
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<td><math>0^{159684}, 2^{79590}, 4^{17871}, 6^{3283}, 8^{700}, 10^{273}, 12^{147}, 14^{84}</math></td>
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</tr>
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<tr>
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<td>9.5</td>
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<td><math>\alpha^{73}x^{136} + \alpha^{146}x^{66} + \alpha^{219}x^{10} + x^3</math></td>
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<td>I 16</td>
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<td><math>0^{159908}, 2^{79086}, 4^{18081}, 6^{3353}, 8^{721}, 10^{336}, 12^{105}, 14^{21}, 16^{21}</math></td>
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</tr>
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<tr>
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<td>9.6</td>
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<td><math>x^{264} + \alpha^{73}x^{96} + \alpha^{219}x^{68} + x^5</math></td>
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<td>I 11</td>
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<td><math>0^{160020}, 2^{79023}, 4^{17997}, 6^{3213}, 8^{868}, 10^{378}, 12^{133}</math></td>
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</tr>
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<tr>
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<td>9.7</td>
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<td><math>\alpha^{219}x^{136} + x^{10} + x^3</math></td>
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<td>I 12</td>
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<td><math>0^{160657}, 2^{77910}, 4^{18312}, 6^{3360}, 8^{952}, 10^{273}, 12^{147}, 14^{21}</math></td>
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</tr>
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<tr>
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<td>9.8</td>
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<td><math>x^{192} + x^{66} + x^{17} + \alpha^{73}x^{10} + x^3</math></td>
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<td>I 14</td>
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<td><math>0^{162183}, 2^{76482}, 4^{17388}, 6^{3871}, 8^{1162}, 10^{252}, 12^{126}, 14^{126}, 16^{21}, 22^{21}</math></td>
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</tr>
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<tr>
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<td>9.9</td>
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<td><math>\alpha^{73}x^{192} + x^{136} + \alpha^{365}x^{129} + x^{17} + x^3</math></td>
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<td>I 5</td>
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<td><math>0^{162708}, 2^{77175}, 4^{15498}, 6^{4270}, 8^{1260}, 10^{252}, 12^{168}, 14^{84}, 16^{126}, 18^{42}, 22^{42}, 26^7</math></td>
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</tr>
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<tr>
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<td>9.10</td>
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<td><math>\alpha^{73}x^{129} + \alpha^{292}x^{66} + x^{10} + x^3</math></td>
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<td>I 9</td>
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<td><math>0^{163009}, 2^{75537}, 4^{17283}, 6^{4116}, 8^{1071}, 10^{168}, 12^{231}, 14^{28}, 16^{84}, 18^{63}, 20^{42}</math></td>
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</tr>
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<tr>
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<td>9.11</td>
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<td><math>x^{80} + \alpha^{146}x^{66} + \alpha^{73}x^{24} + x^{17}</math></td>
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<td>I 13</td>
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<td><math>0^{163366}, 2^{75117}, 4^{17010}, 6^{4536}, 8^{966}, 10^{252}, 12^{63}, 14^{154}, 16^{63}, 18^{84}, 22^{21}</math></td>
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</tr>
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<tr>
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<td>9.12</td>
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<td><math>x^{129} + \alpha^{73}x^{66} + x^{17} + x^{10} + \alpha^{365}x^3</math></td>
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<td>I 6</td>
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<td><math>0^{163996}, 2^{74802}, 4^{16380}, 6^{4368}, 8^{1449}, 10^{231}, 12^{126}, 14^{84}, 16^{42}, 18^{84}, 20^{42}, 22^{21}, 32^7</math></td>
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</tr>
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<tr>
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<td>9.13</td>
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<td><math>\alpha^{73}x^{136} + \alpha^{219}x^{66} + \alpha^{438}x^{10} + x^3</math></td>
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<td>I 15</td>
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<td><math>0^{168994}, 2^{68712}, 4^{15141}, 6^{6279}, 8^{1659}, 10^{336}, 12^{21}, 14^{21}, 16^{105}, 18^{147}, 20^{189}, 24^{21}, 26^7</math></td>
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</tr>
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<tr>
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<td>9.14</td>
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<td><math>\alpha^{438}x^{129} + x^{66} + \alpha^{219}x^{17} + x^3</math></td>
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<td>I 2</td>
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<td><math>0^{169428}, 2^{68040}, 4^{15561}, 6^{6034}, 8^{1533}, 10^{420}, 12^{126}, 14^{21}, 16^{84}, 18^{189}, 20^{126}, 22^{63}, 26^7</math></td>
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</tr>
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<tr>
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<td>9.15</td>
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<td><math>\alpha^{365}x^{80} + \alpha^{292}x^{24} + \alpha^{219}x^{17} + x^3</math></td>
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<td>I 17</td>
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<td><math>0^{170079}, 2^{66297}, 4^{16737}, 6^{6160}, 8^{1407}, 10^{420}, 12^{21}, 14^{42}, 16^{63}, 18^{210}, 20^{133}, 22^{63}</math></td>
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</tr>
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<tr>
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<td>9.16</td>
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<td><math>x^{257} + \alpha^{438}x^{68} + \alpha^{219}x^{12} + x^5</math></td>
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<td>I 7</td>
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<td><math>0^{171430}, 2^{64617}, 4^{16842}, 6^{5733}, 8^{1932}, 10^{483}, 12^{105}, 14^{21}, 16^{147}, 18^{105}, 20^{154}, 22^{21}, 24^{42}</math></td>
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</tr>
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<tr>
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<td>9.17</td>
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<td><math>x^{80} + \alpha^{73}x^{66} + x^{17} + \alpha^{73}x^{10} + x^3</math></td>
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<td>B 31</td>
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<td><math>0^{160440}, 2^{78834}, 4^{17514}, 6^{3388}, 8^{777}, 10^{483}, 12^{126}, 14^{49}, 16^{21}</math></td>
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</tr>
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<tr>
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<td>9.18</td>
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<td><math>\alpha^{365}x^{136} + x^{129} + \alpha^{73}x^{80} + x^{24} + x^{17} + x^3</math></td>
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<td>B 34</td>
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<td><math>0^{164199}, 2^{76734}, 4^{13524}, 6^{4312}, 8^{2205}, 12^{147}, 16^{294}, 18^{147}, 20^{49}, 22^{21}</math></td>
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</tr>
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<tr>
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<td>9.19</td>
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<td><math>\alpha^{73}x^{320} + x^{96} + \alpha^{219}x^{68} + x^{40} + x^{33} + x^5</math></td>
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<td>B 35</td>
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<td><math>0^{172557}, 2^{68355}, 4^{12201}, 6^{3871}, 8^{1638}, 10^{735}, 12^{1470}, 14^{49}, 16^{147}, 18^{441}, 20^{147}, 42^{21}</math></td>
 
</tr>
 
</tr>
 
</table>
 
</table>

Revision as of 18:42, 1 September 2021

ID Representative Equivalent to Orthoderivative diff. spec.
8.1 SW 19
8.2 SW 11
8.3 SW 13
8.4 SW 12
8.5 SW 6
8.6 SW 8
8.7 new
8.8 SW 9
8.9 SW 17
8.10 SW 10
8.11 SW 16
8.12 SW 22
8.13 B 31
8.14 B 12668
8.15 Y 4346
8.16 SW 20
ID Representative Equivalent to Orthoderivative diff. spec.
9.1 I 4
9.2 I 8
9.3 I 3
9.4 I 10
9.5 I 16
9.6 I 11
9.7 I 12
9.8 I 14
9.9 I 5
9.10 I 9
9.11 I 13
9.12 I 6
9.13 I 15
9.14 I 2
9.15 I 17
9.16 I 7
9.17 B 31
9.18 B 34
9.19 B 35